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An idealized LC circuit of zero resistance can oscillate without any source of emf by shifting the energy stored in the circuit between the electric and magnetic fields. In such an LC circuit, if the capacitor contains a charge q before the switch is closed, then all the energy of the circuit is initially stored in the electric field of the capacitor. This energy is given by
02:54Trends in Lattice Energy: Ion Size and Charge
An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:
01:20Mechanisms of Heat Transfer II
In convection, thermal energy is carried by the large-scale flow of matter. Ocean currents and large-scale atmospheric circulation, which result from the buoyancy of warm air and water, transfer hot air from the tropics toward the poles and cold air from the poles toward the tropics. The Earth’s rotation interacts with those flows, causing the observed eastward flow of air in the temperate zones. Convection dominates heat transfer by air, and the amount of available space for the airflow...
01:14Mechanisms of Heat Transfer I
Just as interesting as the effects of heat transfer on a system are the methods by which the heat transfer occur. Whenever there is a temperature difference, heat transfer occurs. It may occur rapidly, such as through a cooking pan, or slowly, such as through the walls of a picnic ice box. So many processes involve heat transfer that it is hard to imagine a situation where no heat transfer occurs. Yet, every heat transfer takes place by only three methods: conduction, convection, and radiation.
01:27Lattice Energies of Ionic Crystals
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01:14Mechanisms of Heat Transfer
Heat transfer between the human body and its environment occurs through four main mechanisms: conduction, convection, radiation, and evaporation.
Conduction, accounting for approximately 3% of body heat loss at rest, is the process of exchanging heat between molecules of two materials in direct contact. This can result in both heat loss and gain. For instance, when the body is submerged in water, which conducts heat 20 times more effectively than air, it can either lose or gain significant heat.
Conduction, accounting for approximately 3% of body heat loss at rest, is the process of exchanging heat between molecules of two materials in direct contact. This can result in both heat loss and gain. For instance, when the body is submerged in water, which conducts heat 20 times more effectively than air, it can either lose or gain significant heat.
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Continuum and lattice heat currents for oscillator chains.
1Department of Physics, University of California, Santa Cruz, California 95064, USA.
Summary
Two definitions of heat current yield different heat conductivity results for oscillator chains. This discrepancy, significant for small systems, depends on chain length and boundary conditions.
Area of Science:
- Condensed matter physics
- Statistical mechanics
- Thermodynamics
Background:
- Heat conductivity is a crucial property for understanding thermal transport in materials.
- The Kubo formula provides a theoretical framework for calculating transport coefficients, including heat conductivity.
- Discrepancies in theoretical calculations can arise from differing definitions of fundamental quantities.
Purpose of the Study:
- To investigate the impact of different heat current definitions on calculated heat conductivity.
- To analyze the dependence of these discrepancies on system size and boundary conditions in oscillator chains.
Main Methods:
- Utilizing the Kubo formula to calculate heat conductivity.
- Comparing results obtained from two distinct definitions of heat current.
- Analyzing finite oscillator chains with different boundary conditions (tethered ends, constant pressure).
Main Results:
- Two common heat current definitions produce different heat conductivity values for finite oscillator chains.
- The discrepancy scales as O(1/N) for chains with tethered ends, where N is the number of particles.
- For chains at constant pressure, the difference decays more slowly, consistent with O(1/N^eta) where 1>eta>0.5.
Conclusions:
- The choice of heat current definition is critical for accurate heat conductivity calculations, especially in finite systems.
- Theoretical models must carefully consider the definition of heat current when applied to nanoscale or mesoscopic systems.
- Further research is needed to establish a universally accepted definition for heat current in diverse physical scenarios.